On the magnitudes of some small cyclotomic integers

• Autorzy: Frederick Robinson , Michael Wurtz
• Języki publikacji: EN

Abstrakty

EN

We prove the last of five outstanding conjectures made by R. M. Robinson from 1965 concerning small cyclotomic integers. In particular, given any cyclotomic integer β all of whose conjugates have absolute value at most 5, we prove that the largest such conjugate has absolute value of one of four explicit types given by two infinite classes and two exceptional cases. We also extend this result by showing that with the addition of one form, the conjecture is true for β with magnitudes up to 5 + 1/25.

Kategorie tematyczne

• 11R18: Cyclotomic extensions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 160
• Numer: 4
• Strony: 317-332

Daty

wydano

2013

Twórcy

autor

Frederick Robinson

• Department of Mathematics, UCLA, Box 951555 Los Angeles, CA, U.S.A.

autor

Michael Wurtz

• Microsoft Corporation, 1 Microsoft Way miwurtz 36/3511, Redmond, WA 98052, U.S.A.

Identyfikatory

DOI

10.4064/aa160-4-2